1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: I need help on solving inequalities?

  1. Oct 27, 2005 #1
    I need help on solving inequalities? Someone please help me. I 'm currently taking Pre-calculus. :smile:
  2. jcsd
  3. Oct 27, 2005 #2

  4. Oct 27, 2005 #3
    equations like the one implied ,
  5. Oct 27, 2005 #4
    This is the way described through my math teachers, although it is not exactly the method I use now.
    First, solve the problem as if it were a normal equality.
    and you get
    [tex]x_1=1 x_2=-3[/tex]
    Now, write down all sets of numbers between those.
    Now set up a table like so
    .....set.....|||||||||||sample point|||||||||||(x-1)|||||||||||(x+3)|||||||||||+ or - ?

    Now, since it was greater than or equal to, you know it has to be greater than zero, therefore the positive ones are the ones you want.

    Therefore, the two sets [tex](-\infty,-3][/tex] and [tex][1,\infty)[/tex] work.

    Now, you know that your answer is [tex](-\infty,-3]\cup[1,\infty)[/tex]

    now, try to solve this one on your own

    Last edited: Oct 27, 2005
  6. Oct 27, 2005 #5
    You can do the familiar algebraic manipulation with inequalities, provided you remember to reverse the direction of the inequality whenever you multiply (or divide) by a negative quantity and practice simple logic. So by the example above,
    [tex]x^2+2x-3 \geq 0[/tex]
    [tex](x-1)(x+3) \geq 0[/tex]
    Now, if [itex]ab \geq 0[/itex], either ([itex]a \geq 0[/itex] and [itex]b \geq 0[/itex]) or ([itex]a \leq 0[/itex] and [itex]b \leq 0[/itex]) as you should easily justify. Let's evaluate the first set:
    [itex]x-1 \geq 0[/itex] and [itex]x+3 \geq 0[/itex]
    implies that
    [itex]x \geq 1[/itex] and [itex]x \geq -3[/itex]
    which is the set [itex]\{x: x \geq 1\}[/itex]. Remember that x must satisfy both inequalities when using "and".
    The second set evaluates to [itex]\{x: x \leq -3\}[/itex], so we have the set [itex]\{x: x \geq 1[/itex] or [itex]x \leq -3\}[/itex], or written another way [itex]\{x: x \geq 1\} \cup \{x: x \leq -3\}[/itex].
    This is just the purely algebraic way. Choose whichever way you feel most comfortable with. :smile:
    Last edited: Oct 28, 2005
  7. Oct 28, 2005 #6
    My favorite word: VISUALIZE.

    For generic inequality
    [tex]f(x) > g(x)[/tex]:
    [tex]h(x) = f(x) - g(x)[/tex].
    Find the intervals where a graph [tex]y=h(x)[/tex] is above the x-axis (you'll have to find/estimate the roots of the [tex]y=h(x)[/tex] and points where [tex]h(x)[/tex] is undetermined).

    [tex]\frac{x+2}{x}\leq \frac{1}{2-x}[/tex]
    Could you post your answer?
    Last edited: Oct 28, 2005
  8. Oct 28, 2005 #7
    gosh, that looks confusing!

    i was just taught to regard the inequality as a quadratic, make it equal to 0, draw the graph and solve it from there.

    that may be what ^^ was saying though...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook